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Comput Phys Commun. 2017 Oct;219:87-90. doi: 10.1016/j.cpc.2017.05.010. Epub 2017 May 22.

Sampling random directions within an elliptical cone.

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Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114, USA.


This work extends the spherical surface sampling algorithm in order to uniformly generate random directions within an elliptical cone. This has applications in Monte Carlo particle transport simulations, for example modeling asymmetric beam divergence or scattering interactions. Two methods are presented. The first obeys the strict boundary of the elliptical cone. The second relaxes this requirement, increasing the range of generated directions by up to 10% for elliptical cones of extreme eccentricity. However, the second method is able to generate directions beyond the equator.


Monte Carlo; random direction; spherical sampling

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